The optimal aspect ratio for piecewise quadratic anisotropic finite element approximation

Mesh adaptation for finite element approximation is a procedure used in numerous applications. The use of thin and long anisotropic triangles improves the efficiency of the procedure. When piecewise linear finite elements are used, the aspect ratio for mesh adaptation is generally dictated by the absolute value of the (estimated) hessian matrix of the approximated function. We give in this paper the corresponding aspect ratio for piecewise quadratic finite elements.